A commentary I am reading says that the Present Tense of ANAKAINOUTAI
coupled with the idiom hHMERAi KAI hHMERAi would imply something
that is renewed all over again each day, rather than an on-going process.

This act of renewing is something we are to undertake each day. According to
the commentary, this is not an on-going renewal process
that would have some gradual increase or decrease over a period of time.
I get the impression that he believes this act of renewal enters us into a
renewed "state" each day. And that "state" only last one day. We must renew
day after day.